A quick answer would "no"... but as always, there is plenty room for moderation. (Note: I'm not a biker, but...)
First thing to know, the French route and the routes in Spain(-Portugal) are not comparable when talking about the paths and their physical features. Advises can not apply to one another. The Caminos in France are
mapped for hikers through the most natural path possible, while in Spain, they are
build to allow everyone to use them or use existing roads. There are exceptions of course, but that's the general idea. The French GR are indeed made by the FFRP, the French Federation for
Pedestrian Trails.
Bikers are extremely rare on Le Puy route and when I come to think of it, I've never seen any while walking... The ones who "do it" actually mostly do a side-Camino. Also, guidebooks and those who did it this way advise not to do it a beginners, but to have a good experience of (moutain) biking... do you have it?
On the stretch from Le Puy to ~Moissac, it's mostly not possible to follow the same path than the pilgrims on foot, unless you have (quoting the Miam Miam Dodo, greatest guidebook reference for this route) a "death wish". This is the central mountain of France, so the landscape is mostly uneven and steep whether you go up or gown. There are many un-doable stretches. You'll have to take the road
a lot, missing the most emblematic part of this Camino.
From ~Moissac to SJPdP, you're out of of the mountains. It's still very hilly with lots of delicate parts, but obviously more doable.
Like I said, I'm not a biker. However, I've walked Le Puy and found it hard enough on foot as it is: I personally would
not do it with a loaded bike! Travel agencies who offer to do this route by bike make people take mostly the road. I also invite you to Google-translate theses pages by 2 French bikers who did Le Puy route: (certainly a goldmine of tips!)
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Le Puy to Cahors ~~
Cahors to Ostabat ~~
Ostabat to SJPdP
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More info and details on this website
I don't know much about bikes, but from what I get, a VTT (mountain bike) and VTC (all-ways bike) are not the same. And a VTT seems to be a way better option for Le Puy route than a VTC... But again, I'm really not a specialist... Note that if you buy your bikes in France, you'll most likely have to deal with non-English speaker!
I'd advise you to get a map where you can see the Camino, but more importantly, the roads around. Here's a book (in French...) dedicated to the
Le Puy route by bike.
Finally, know that planning may be tricky, as pilgrims on foot have priority on those with a bike. Be sure to tell the accommodation owners you're on bike! It may prevent you from bad surprises...
I hope you don't find this post too dark!
I wish you a nice (and strong!) preparation, and to enjoy your Camino!
Bon Chemin!